@0celo7 The string perturbation series is also an expansion around the "classical free background" of string theory, which is essentially given by the precise choice of CFT that lives on the world sheets.
@0celo7 Well, one can define a CFT purely by the central charge and the conformal weights, since these fix the structure of the space of states (the space of states has to be a unitary representation of the Virasoro algebra, and generic ladder operator methods show those representations can be labeled by $c$ and the allowed conformal weights (and only certain weights are possible for certain charges to begin with)). But I'm not sure that's what the string people mean by choice of CFT
(Since charge and weights are fixed by ST AFAIK)
I'm also unsure how the fermions appear in this way.
@0celo7 Okay, then $h$ and $g$ tell you how often you have to go around the torus until the boundary values are equal. The modular transformation just changes the size of the torus, but not its modular structure. So on a torus with a different size, the same field has to go around the torus a different number of times to be equal because the torus is larger/smaller.
That is, if we phrase the tori as lattices in the complex plane (spanned by $\lambda_1,\lambda_2$), then the function $\psi$ is always periodic with the period length $n_i\lambda_i$, where $n_i$ is given by solving $h^{n_i} = 1$.
@Danu : not so, I give robust references to support the answers I give. There's nothing controversial about things like the speed of a light wave depends on the strength of the gravitational potential. But I see this sort of thing getting downvoted by mathematical kids whose arrogance is only exceeded by their ignorance, and who lap up popscience trash whilst dismissing Einstein and the evidence. I've seen similar re other posters. They give a rock-solid correct answer, but some patent blatant wrong answer gets the upvotes. — John Duffield1 min ago
When an unclear or otherwise lacking question is posted on this site, it often happens that one of the more experienced users posts a comment asking for clarification. Fairly often, the asker responds in a comment to the original post, attempting to clarify or otherwise improve the question. With...
@0celo7 : the physics I talk about is is mainstream physics. I'm the one who refers to "Einstein and the evidence". You're the one who dismisses it. Sheesh, yesterday one of you was dismissing the wave nature of matter. :rolleyes:
@JohnDuffield Electron = photon going around a Dirac belt is mainstream?
@JohnDuffield For someone who asserts his intellectual superiority over many of the twentieth century's greatest physicists on a daily basis, I think are being very harsh about the "arrogance" and "ignorance" of the user base of this site. — Danu11 mins ago
@0celo7: Pair production is mainstream. The wave nature of matter is mainstream. Electron diffraction is mainstream. Spin ½ is mainstream. The Dirac wave equation is mainstream.
@0celo7 : no you don't. What you "know" about black holes is wrong. And puhlease, don't come out with phrases like "surpisingly intelligent" when talking about people like Rovelli.
@0celo7 : it's called gamma-gamma pair production, and it works becuase displacement current does what it says on the can. See how Wikipedia says pair production occurs because pair production occurs spontaeously? Like worms from mud? That's cargo-cult trash, and that turbine hum you can hear is Feynman turning in his grave.
@JohnDuffield You don't understand QED, the theory Feynman got so famous for. Yet you have the audacity to use him in an appeal to authority to make a point that goes against the principles of QED. Good job.
@0celo7 : so think it through. What happened to the +511keV photon? Did it magically disappear? Did the electron magically pop into existence courtesy of some "God did it" creation operator? What happens in annihilation? Let's see now, we started with a wave going thataway, we ended up with a wave going thisaway, and in between we had... a point particle made of cheese!
@Danu Oops. Sorry for the confusion. As mentioned I use this website rarely, am not familiar with many of its features, and it's been a long day. Anyway, I think I've said enough. It's back to the salt mine for me. – Michael A. Gottlieb 1 min ago
@Danu : I understand it, and I've read his little books. And nothing that I've said goes against the principles of QED. Nothing. What goes against the principles of QED is cargo-cult nonsense peddled by popscience quacks.
@Danu Well, probably not; but they have rules that are not written. There is a lot of probability that your first referee will dub the paper as obscure and involved
even if in your opinion was pure source water clear
@FenderLesPaul To most Europeans, that comes across as pretty narrow-minded.
3
user54412
I can understand forcing a second language in high school, just like we force students to learn chemistry and history and maybe even a bit of music, for the purpose of breadth.
user54412
But the whole "learn something other than English so you can communicate" was one of the most ridiculous lies I was told as a child.
@FenderLesPaul In a PhD in mathematics, I can see how it'd be useful. I don't know what you're doing in life, so I can't go into the specifics for you particularly.
user54412
5:39 PM
@Danu I think that says more about the stubborn old-fashionedness of mathematicians than about the the usefulness of French ;)
@ChrisWhite Yeah, that's not true. Communicating in English is fine most of the time---but just in order to realize what else is out there and maybe even read something in a different langauge is pretty nice.
like spanish 1 here had 1 lecture and 4 discussions a week and HW everyday
it was insane
and we are required to take 3 semesters of language
user54412
Keep in mind that in the US, it's not like you can go and practice most languages outside of class. It's pretty hard to master a language when your teacher is the only person you know who speaks it.
I should note though that my main complaint of workload is not really restricted to language so I don't want to come off as criticizing mandatory language classes specifically
user54412
5:44 PM
@Danu When choosing what college to go to I almost went somewhere else that had a much broader language program. I actually wanted to learn some dead languages for fun.
The highest level of high school education (it is split in several disconnected programs in Holland; kids get grouped based on test scores from before etc.) requires either Latin (6 years) or Ancient Greek (5 years).
user54412
both of which are apparently more useful than Dutch :P
Warning: this comic occasionally contains strong language (which may be unsuitable for children), unusual humor (which may be unsuitable for adults), and advanced mathematics (which may be unsuitable for liberal-arts majors).
The Veronese Riddle is a riddle written in late Vulgar Latin written on the margin of a parchment, on the Verona Orational, probably in the 8th or early 9th century, by a Christian monk from Verona, in northern Italy. It was a very popular riddle in the Middle Ages and has survived into dialects to date. Discovered by Luigi Schiaparelli in 1924, it is considered the first document ever written in the Italian language along with the Placiti Cassinesi.
== Text ==
Original Text:
Se pareba boves
alba pratalia araba
albo versorio teneba
negro semen seminaba
Rough Translation:
In front of him (he) led...
We consider the metric
$$\mathrm{d}s^2=-\mathrm{d}t^2+a^2(t)\mathrm{d}\vec x^2 $$
where $a(t):= a_0e^{Ht}$. To show that these coordinates do not cover the entire spacetime manifold, we consider the trajectory of a freely falling observer, which of course extremizes the proper time
$$\tau=\int...
@DanielSank You expressed interest in this answering-unanswered-questions type of thing, right? Who else starred my comment (there were a lot of stars!)?
Guys, over at TeX - LaTeX they have this (weekly?) session called "answer the unanswered" which means a bunch of (serious) users get together in chat and try to answer a whole bunch of questions that have either been answered in the comments, are easy to answer, etc; sometimes they also vote to delete an old unanswered question that is deemed too bad. What do you guys think about potentially doing this here on PSE?
Hawking-Ellis shows that that form of the metric is obtained from the embedding equation in $\mathbb{R}^5$ and that the coordinates are simply not defined everywhere.
Ah, it seems OP is insisting on doing it using the geodesic equation.
> partially to prevent this answer from being abused by lazy students